Dimension estimation (DE) is the process of determining the intrinsic dimensionality of data (e.g., see Chapter 3 in [1]}). Usually, real world datasets have large numbers of features, often significantly greater than the number of latent factors underlying the data generating process, and DE attempts to quantify the number of latent factors in a dataset. Of course, latent factors are often discussed in relation a linear analysis. However, such ideas can be generalized to a non-linear context, and such generalizations will be our focus here. For example, in an image processing problem each pixel of an image can be thought of a feature that one measures about the image. However, the measured pixels are not independent of each other since, for example, nearby pixels are likely to have similar colors.
Accordingly, it can be quite useful to estimate the underlying latent factors, such as pose and lighting, that effect many pixels simultaneously.
